{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T19:10:17Z","timestamp":1737227417909,"version":"3.33.0"},"reference-count":18,"publisher":"Wiley","issue":"13","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":5558,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp; Computers in Japan"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the real world, there are many propositions which cannot be determined to be true or false. In order to treat such propositions, multivalued logic systems which are permitted to take more than true (1) or false (0) values have been developed. In this paper, we will describe fundamental properties of multivalued Kleenean functions, which are effective for treating ambiguity. First, we will introduce a partial order relation into the set of truth values {0, 1\/(<jats:italic>m<\/jats:italic>\u2010 1), \u2026, (<jats:italic>m<\/jats:italic>\u2010 2)\/(<jats:italic>m<\/jats:italic>\u2010 1), 1}. It will be shown that any multivalued Kleenean function is monotone for this partial order relation. Next, it will be shown that any multivalued Kleenean function can be determined uniquely for inputs {0, 1\/2, 1} only. Finally, we will describe P\u2010type logic functions for multivalued Kleenean functions which are capable of correcting input failures.<\/jats:p>","DOI":"10.1002\/scj.4690231306","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T22:44:20Z","timestamp":1183848260000},"page":"66-75","source":"Crossref","is-referenced-by-count":2,"title":["Fundamental properties of multivalued kleenean functions"],"prefix":"10.1002","volume":"23","author":[{"given":"Noboru","family":"Takagi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masao","family":"Mukaidono","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"issue":"6","key":"e_1_2_1_2_2","first-page":"355","article-title":"On the B\u2010ternary logic functions\u2014A ternary logic for considering ambiguity","volume":"55","author":"Mukaidono M.","year":"1972","journal-title":"Trans. I.E.C.E., Japan"},{"key":"e_1_2_1_3_2","unstructured":"M.MukaidonoandI. G.Rosenberg.K\u2010valued functions for treating ambiguities\u2014Their clone and a normal form. In: Proc. IEEE 16th Int. Symp. Multivalued Logic pp.204\u2013211(May1986)."},{"issue":"3","key":"e_1_2_1_4_2","first-page":"150","article-title":"On some properties of fuzzy logic","volume":"58","author":"Mukaidono M.","year":"1975","journal-title":"Trans. I.E.C.E., Japan"},{"issue":"12","key":"e_1_2_1_5_2","first-page":"748","article-title":"An algebraic structure of fuzzy logical functions and its minimal and irredundant form","volume":"58","author":"Mukaidono M.","year":"1975","journal-title":"Trans. I.E.C.E., Japan"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1986.1676738"},{"key":"e_1_2_1_7_2","unstructured":"M.Mukaidono.A necessary and sufficient condition for fuzzy logic functions. In: Proc. IEEE 9th Int. Symp. Multivalued Logic pp.159\u2013166(May1979)."},{"key":"e_1_2_1_8_2","unstructured":"M.Mukaidono.A set of independent and complete axioms for a fuzzy algebra (Kleene algebra). In: Proc. IEEE 11th Int. Symp. Multivalued Logic pp.27\u201334(May1981)."},{"key":"e_1_2_1_9_2","first-page":"332","volume-title":"Introduction to Metamathematics","author":"Kleene S. C.","year":"1952"},{"issue":"7","key":"e_1_2_1_10_2","first-page":"517","article-title":"A quantization theorem in fuzzy logic","volume":"39","author":"Mukaidono M.","year":"1975","journal-title":"Bulletin of Electrotechnical Laboratory, Japan"},{"key":"e_1_2_1_11_2","unstructured":"T.Araki.A research on fuzzy logic functions with constants. Master's Thesis Meiji University (1987)."},{"key":"e_1_2_1_12_2","unstructured":"Y.YamamotoandM.Mukaidono.P\u2010type logic functions\u2014Ternary logic functions capable of correcting input failures. In: Proc. IEEE 17th Int. Symp. Multivalued Logic pp.161\u2013169(May1987)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","unstructured":"Y.YamamotoandM.Mukaidono.Ambiguity decision tables and P\u2010ternary logic functions. In: Proc. IEEE Int. Symp. Multivalued Logic pp.338\u2013345(May1988).","DOI":"10.1109\/ISMVL.1988.5192"},{"issue":"6","key":"e_1_2_1_14_2","first-page":"439","article-title":"Three\u2010valued majority functions","volume":"63","author":"Yamamoto Y.","year":"1980","journal-title":"Trans. I.E.C.E., Japan"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/12.2225"},{"issue":"12","key":"e_1_2_1_16_2","first-page":"2517","article-title":"p\u2010valued logical functions derived from two\u2010valued input p\u2010valued output functions and determination of their logical formulae","volume":"71","author":"Hata Y.","year":"1988","journal-title":"Trans. I.E.I.C.E., Japan"},{"issue":"3","key":"e_1_2_1_17_2","article-title":"On some rules for deriving p\u2010valued logical functions from two\u2010valued input p\u2010valued output functions","volume":"13","author":"Yamato K.","year":"1988","journal-title":"Note on Multivalued Logic in Japan"},{"issue":"2","key":"e_1_2_1_18_2","first-page":"183","article-title":"Identification for multivalued Kleenean functions and determination of their logical formulae","volume":"73","author":"Hata Y.","year":"1990","journal-title":"Trans. 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