### Abstract

The main purpose of this paper is to establish conditions under which the Jensen type inequality for the discrete bipolar pseudo-integral is valid. Besides, we extend investigations of the properties of the bipolar pseudo-integral. The observations concern the discrete bipolar pseudo-integrals based on the following three canonical cases of two binary symmetric operations: in the first case they are generated by an odd, strictly increasing and continuous function, in the remaining two cases a symmetric-addition is the symmetric maximum, while in the second case the corresponding pseudo-multiplication is a non-idempotent operation, and in the third case it is the symmetric minimum.

Original language | English |
---|---|

Journal | Fuzzy Sets and Systems |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- Bi-capacity
- Bipolar pseudo-integral
- Jensen-Steffensen's inequality
- Symmetric pseudo-addition
- Symmetric pseudo-multiplication

### ASJC Scopus subject areas

- Logic
- Artificial Intelligence

### Cite this

*Fuzzy Sets and Systems*. https://doi.org/10.1016/j.fss.2019.04.015

**Jensen type inequality for the bipolar pseudo-integrals.** / Todorov, Miloš; Štrboja, Mirjana; Pap, E.; Mihailović, Biljana.

Research output: Contribution to journal › Article

*Fuzzy Sets and Systems*. https://doi.org/10.1016/j.fss.2019.04.015

}

TY - JOUR

T1 - Jensen type inequality for the bipolar pseudo-integrals

AU - Todorov, Miloš

AU - Štrboja, Mirjana

AU - Pap, E.

AU - Mihailović, Biljana

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The main purpose of this paper is to establish conditions under which the Jensen type inequality for the discrete bipolar pseudo-integral is valid. Besides, we extend investigations of the properties of the bipolar pseudo-integral. The observations concern the discrete bipolar pseudo-integrals based on the following three canonical cases of two binary symmetric operations: in the first case they are generated by an odd, strictly increasing and continuous function, in the remaining two cases a symmetric-addition is the symmetric maximum, while in the second case the corresponding pseudo-multiplication is a non-idempotent operation, and in the third case it is the symmetric minimum.

AB - The main purpose of this paper is to establish conditions under which the Jensen type inequality for the discrete bipolar pseudo-integral is valid. Besides, we extend investigations of the properties of the bipolar pseudo-integral. The observations concern the discrete bipolar pseudo-integrals based on the following three canonical cases of two binary symmetric operations: in the first case they are generated by an odd, strictly increasing and continuous function, in the remaining two cases a symmetric-addition is the symmetric maximum, while in the second case the corresponding pseudo-multiplication is a non-idempotent operation, and in the third case it is the symmetric minimum.

KW - Bi-capacity

KW - Bipolar pseudo-integral

KW - Jensen-Steffensen's inequality

KW - Symmetric pseudo-addition

KW - Symmetric pseudo-multiplication

UR - http://www.scopus.com/inward/record.url?scp=85064468259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064468259&partnerID=8YFLogxK

U2 - 10.1016/j.fss.2019.04.015

DO - 10.1016/j.fss.2019.04.015

M3 - Article

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

SN - 0165-0114

ER -